共查询到20条相似文献,搜索用时 125 毫秒
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无网格方法数值结果的可视化方法与实现 总被引:4,自引:0,他引:4
科学计算可视化是科学计算中不可缺少的一个组成部分,其主要任务是将数值模拟产生的大量复杂的数据信息通过计算机技术转换成图形、图像信息。无网格方法是一种基于点的数值计算方法,各离散点之间没有联结信息,其数值结果的可视化后处理是一件很困难的事情,尤其当离散点随机分布时,更是如此。Delaunay 三角化是十分理想的散乱数据的可视化工具,它可以根据一组随机分布的离散点数据生成唯一的近似等边三角形。首先介绍了 Voronoi 图与 Delaunay 三角化的基本原理,然后介绍了实现 Delaunay 三角剖分的算法及无网格方法数值结果可视化的实现方法,最后给出了无网格方法可视化的若干应用实例。 相似文献
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基于SPH方法的沙粒流体起跳风速的研究 总被引:1,自引:0,他引:1
运用光滑粒子流体动力学(Smoothed Particle Hydrodynamics:SPH)方法对沙粒在气流中的起跳现象进行数值模拟。沙粒的起动风速一直是风沙两相流研究的重点内容。SPH方法将整个计算区域离散成两种分别代表气相的和沙粒相的单个粒子。在气相粒子的作用下,每个沙粒从起跳到在气相粒子的作用下随着气相粒子运动的过程都可以被动态地呈现出来。该文首先介绍了SPH方法基本理论,详细评述了SPH公式中的核心因素及其对数值模拟结果的影响,提出了风沙二相流的SPH数值模型;其次对数值模型进行了离散化,设置边界条件对沙粒的起跳过程进行数值模拟;最后将数值模拟结果与已有的起动风速的实验测量结果及他人的数值模拟结果进行比较,结果表明:用该方法计算的结果与前人所进行的研究结果是一致的,并且得到一些新的结论。 相似文献
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一种新的无网格方法与有限元耦合法 总被引:1,自引:1,他引:0
本文分析了Belytschko和Huerta提出的无网格方法和有限元耦合法各自存在的问题,提出了一种新的无网格方法与有限元耦合法。Belytschko提出的方法的缺点是,无网格方法子域和有限元法子域的界面必须是规则的,交界域内有限元不能随意划分,交界域内无网格方法的节点也不能随意分布。Huerta提出的方法的缺点是对交界域内无网格方法的节点影响域可能无法覆盖交界域。本文提出的无网格方法与有限元耦合法解决了以上两种方法存在的问题,并保留了无网格方法随意配点的优点、交界面可以不规则、提高了无网格子域内的求解精度,从而提高问题的整体求解精度。然后,建立了弹性力学的无网格方法与有限元法的耦合法。最后给出了数值算例。 相似文献
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为了提高无网格方法计算振动问题时的计算效率和计算精度,开发了无网格时域自适应算法。该方法在时域内采用时域自适应算法,将每个变量在每个时间步内离散成关于时间的展开形式,通过控制展开阶数保证自适应算法的精度,可以更准确的描述变量随时间的变化;同时将时空耦合的初值问题转化为一系列的空间边值问题,并采用无网格方法递推求解。该方法可以提高计算效率并弥补时间步长较多或较大时造成的精度损失,并通过数值算例验证了其准确性。 相似文献
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无单元法研究现状及展望 总被引:15,自引:1,他引:14
无单元法是众多无网格方法中较有代表性的一种,形式简单、明确,计算精度高。因其具有仅需离散的结点信息、解答具有高次连续性、能较好地反映应力高梯度分布并便于跟踪裂纹的扩展过程等优点,无单元法自问世以来获得了广泛的重视,已成为计算力学领域的一个研究热点。文中着重分析了无单元法研究中的热点问题及解决方法,介绍了该方法目前的一些应用范围,并指出其可能的发展方向。 相似文献
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Amir Khosravifard Mohammad Rahim Hematiyan 《Engineering Analysis with Boundary Elements》2010,34(1):30-40
A method for the evaluation of regular domain integrals without domain discretization is presented. In this method, a domain integral is transformed into a boundary integral and a 1D integral. The method is then utilized for the evaluation of domain integrals in meshless methods based on the weak form, such as the element-free Galerkin method and the meshless radial point interpolation method. The proposed technique results in truly meshless methods with better accuracy and efficiency in comparison with their original forms. Some examples, including linear and large-deformation problems, are also provided to demonstrate the usefulness of the proposed method. 相似文献
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In this paper, analytical forms of integrals in the meshless local integral equation method in the Laplace space are derived and implemented for elastodynamic problems. The meshless approximation based on the radial basis function (RBF) is employed for implementation of displacements. A weak form of governing equations with a unit test function is transformed into local integral equations. A completed set of the local boundary integrals are obtained in closed form. As the closed form of the local boundary integrals are obtained, there are no domain or boundary integrals to be calculated numerically. Several examples including dynamic fracture mechanics problems are presented to demonstrate the accuracy of the proposed method in comparison with analytical solutions and the boundary element method. 相似文献
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Jianming Zhang Masataka Tanaka Toshiro Matsumoto 《International journal for numerical methods in engineering》2004,59(9):1147-1166
Combining a modified functional with the moving least‐squares (MLS) approximation, the hybrid boundary node method (Hybrid BNM) is a truly meshless, boundary‐only method. The method may have advantages from the meshless local boundary integral equation (MLBIE) method and also the boundary node method (BNM). In fact, the Hybrid BNN requires only the discrete nodes located on the surface of the domain. The Hybrid BNM has been applied to solve 2D potential problems. In this paper, the Hybrid BNM is extended to solve potential problems in three dimensions. Formulations of the Hybrid BNM for 3D potential problems and the MLS approximation on a generic surface are developed. A general computer code of the Hybrid BNM is implemented in C++. The main drawback of the ‘boundary layer effect’ in the Hybrid BNM in the 2D case is circumvented by an adaptive face integration scheme. The parameters that influence the performance of this method are studied through three different geometries and known analytical fields. Numerical results for the solution of the 3D Laplace's equation show that high convergence rates with mesh refinement and high accuracy are achievable. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
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In the present paper the Trefftz function as a test function is used to derive the local boundary integral equations (LBIE)
for linear elasticity. Since Trefftz functions are regular, much less requirements are put on numerical integration than in
the conventional boundary integral method. The moving least square (MLS) approximation is applied to the displacement field.
Then, the traction vectors on the local boundaries are obtained from the gradients of the approximated displacements by using
Hooke's law. Nodal points are randomly spread on the domain of the analysed body. The present method is a truly meshless method,
as it does not need a finite element mesh, either for purposes of interpolation of the solution variables, or for the integration
of the energy. Two ways are presented to formulate the solution of boundary value problems. In the first one the local boundary
integral equations are written in all nodes (interior and boundary nodes). In the second way the LBIE are written only at
the interior nodes and at the nodes on the global boundary the prescribed values of displacements and/or tractions are identified
with their MLS approximations. Numerical examples for a square patch test and a cantilever beam are presented to illustrate
the implementation and performance of the present method.
Received 6 November 2000 相似文献
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Chloride-induced corrosion of steel reinforcements has been identified as one of the main causes of deterioration of concrete structures. A feasible numerical method is required to predict chloride penetration in concrete structures. A transient meshless boundary element method is proposed to predict chloride diffusion in concrete with time dependent nonlinear coefficient. Taking Green's function as the weighted function, the weighted residue method is adopted to transform the diffusion equation into equivalent integral equations. By the coupling of radial integral method and radial basis function approximation, the domain integrals in equivalent control equations are transformed into boundary integrals. Following the general procedure of boundary element meshing and traditional finite difference method, a set of nonlinear algebraic equations are constructed and are eventually solved with the modified Newtonian iterative method. Several numerical examples are provided to demonstrate the effectiveness and efficiency of the developed model. A comparison of the simulated chloride concentration with the corresponding reported experimental data in a real marine structure indicates the high accuracy and advantage of the time dependent coefficient and nonlinear model over the conventional constant coefficient model. 相似文献
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I. V. Singh 《Sadhana》2004,29(3):285-296
This paper deals with the solution of two-dimensional fluid flow problems using the meshless element-free Galerkin method.
The unknown function of velocity u(x) is approximated by moving least square approximants uh(x). These approximants are constructed by using a weight function, a monomial basis function and a set of non-constant coefficients.
The variational method is used for the development of discrete equations. The Lagrange multiplier technique has been used
to enforce the essential boundary conditions. A new exponential weight function has been proposed. The results are obtained
for a two-dimensional model problem using different EFG weight functions and compared with the results of finite element and
exact methods. The results obtained using proposed weight functions (exponential) are more promising as compared to those
obtained using existing weight functions (quartic spline and Gaussian) 相似文献
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Moving least squares approximation (MLSA) has been widely used in the meshless method. The singularity should appear in some special arrangements of nodes, such as the data nodes lie along straight lines and the distances between several nodes and calculation point are almost equal. The local weighted orthogonal basis functions (LWOBF) obtained by the orthogonalization of Gramm–Schmidt are employed to take the place of the general polynomial basis functions in MLSA. In this paper, MLSA with LWOBF is introduced into the virtual boundary meshless least square integral method to construct the shape function of the virtual source functions. The calculation format of virtual boundary meshless least square integral method with MLSA is deduced. The Gauss integration is adopted both on the virtual and real boundary elements. Some numerical examples are calculated by the proposed method. The non-singularity of MLSA with LWOBF is verified. The number of nodes constructing the shape function can be less than the number of LWOBF and the accuracy of numerical result varies little. 相似文献
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K. M. Liew Yumin Cheng S. Kitipornchai 《International journal for numerical methods in engineering》2006,65(8):1310-1332
In this study, we first discuss the moving least‐square approximation (MLS) method. In some cases, the MLS may form an ill‐conditioned system of equations so that the solution cannot be correctly obtained. Hence, in this paper, we propose an improved moving least‐square approximation (IMLS) method. In the IMLS method, the orthogonal function system with a weight function is used as the basis function. The IMLS has higher computational efficiency and precision than the MLS, and will not lead to an ill‐conditioned system of equations. Combining the boundary integral equation (BIE) method and the IMLS approximation method, a direct meshless BIE method, the boundary element‐free method (BEFM), for two‐dimensional elasticity is presented. Compared to other meshless BIE methods, BEFM is a direct numerical method in which the basic unknown quantity is the real solution of the nodal variables, and the boundary conditions can be applied easily; hence, it has higher computational precision. For demonstration purpose, selected numerical examples are given. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
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Traditional numerical techniques such as FEM and BEM have been successfully applied to the solutions of Biot's consolidation problems. However, these techniques confront some difficulties in dealing with moving boundaries. In addition, pre-designing node connectivity or element is not an easy task. Recently, developed meshless methods may overcome these difficulties. In this paper, a meshless model, based on the local Petrov–Galerkin approach with Heaviside step function as well as radial basis functions, is developed and implemented for the numerical solution of plane strain poroelastic problems. Although the proposed method is based on local boundary integral equation, it does not require any fundamental solution, thus avoiding the singularity integral. It also has no domain integral over local domain, thus largely reducing the computational cost in formulation of system stiffness. This is a truly meshless method. The solution accuracy and the code performance are evaluated through one-dimensional and two-dimensional consolidation problems. Numerical examples indicate that this meshless method is suitable for either regular or irregular node distributions with little loss of accuracy, thus being a promising numerical technique for poroelastic problems. 相似文献